High-order numerical schemes for shallow water equations with variable topography are constructed, based on exact Riemann solvers. The schemes are shown to be well-balanced and can provide us with a good accuracy. Although the schemes are of essentially nonoscillatory (ENO) type, visible oscillations can be observed for these schemes with large orders. Precisely, tests show that a 3rd-order ENO-type scheme provides us with convergence, but large oscillations appear in 5fth-order and 7th-order ENO-type schemes.